Finally, regarding the class (c) of exact nonconvex reformulations, there are, to the best of our knowledge, still just a very few papers providing such reformulations.
A natural choice is to use a mixed-integer program, cf. reformulation REF .
This is useful for finding sparse solutions of – often quadratic – problems, whose dimension is not too large, and allows, in principle, to compute a global minimum, see e.g. [1]}.
By modifying the objective function with a suitable regularizing term, c.f. [2]}, also larger problem dimensions can be handled.
For nonlinear programs or large-scale problems, however, this typically leads to an intractable reformulation.
One alternative approach is the complementarity-type reformulation suggested in [3]}, which can be shown to be
completely equivalent to the original sparse optimization problem REF .
The focus of the paper [3]}, however, is slightly different.
